On Sampling and Coding for Distributed Acoustic Sensing

The issue of how to efficiently represent the data collected by a network of microphones recording spatio-temporal acoustic wave fields is addressed. Each sensor node in the network samples the sound field, quantizes the samples and transmits the encoded samples to some central unit, which computes an estimate of the original sound field based on the information received from all the microphones. Our analysis is based on the spectral properties of the sound field, which are induced by the physics of wave propagation and have a significant impact on the efficiency of the chosen sampling lattice and coding scheme. As field acquisition by a sensor network typically implies spatio-temporal sampling of the field, a multidimensional sampling theorem for homogeneous random fields with compactly supported spectral measures is proved. To assess the loss of information implied by source coding, rate distortion functions for various coding schemes and sampling lattices are determined. In particular, centralized coding, independent coding and some multiterminal schemes are compared. Under the assumption of spectral whiteness of the sound field, it is shown that sampling with a quincunx lattice followed by independent coding is optimal as it achieves the lower bound given by centralized coding.